# “A little knowledge is a dangerous thing. So is a lot.”

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“A little knowledge is a dangerous thing. So is a lot.”
Game Theory Topic 7 Information “A little knowledge is a dangerous thing So is a lot.” - Albert Einstein

Strategic Use of Information
Incentive Schemes Creating situations in which observable outcomes reveal the unobservable actions of the opponents. Screening Creating situations in which the better-informed opponents’ observable actions reveal their unobservable traits. Mike Shor

Signaling Definition Requires
Using actions that other players would interpret in a way that would favor you in the game play Requires It is not in the best interest for people to signal falsely Implies signaling must be costly! Mike Shor

Auto Insurance A \$1,000 deductible? High risk drivers:
30% chance of claim Risk aversion: willing to pay \$500 Low risk drivers: 10% chance of claim Risk aversion: willing to pay \$200 Mike Shor

Pooling vs. Separating A pooling equilibrium has all types taking the same action Therefore, cannot distinguish types by the actions they take A separating equilibrium has different types taking different actions Therefore, can distinguish types by the actions they take Mike Shor

Cost of No Deductible If the cost of avoiding a deductible is
Less than \$200 Both types buy Pooling Equilibrium Greater than \$500 Neither type buys Pooling equilibrium Between \$200 and \$500 Only high risk drivers buy Separating equilibrium Mike Shor

Pooling Insurance company charges \$200
Both types buy Expected profit for insurance company: High risk drivers: \$200 - (30%) \$1,000 = \$200 - \$300 = -\$100 Low risk drivers: \$200 - (10%) \$1,000 = \$200 - \$100 = \$100 Profitable only if there are more low-risk drivers than high-risk drivers Mike Shor

Separating Insurance company charges \$500 Always profitable
Only high-risk drivers buy Expected profit for insurance company: High risk drivers: \$500 - (30%) \$1,000 = \$500 - \$300 = \$200 Low risk drivers: \$0 Always profitable Mike Shor

Comparing Equilibria Imagine that p proportion are high-risk
Insurance company charges \$200 Profit: \$100 (1-p) - \$100 p = \$100-\$200p Insurance company charges \$500 Profit: \$200p Compare: \$200p > \$100-\$200p p > ¼  better to separate than pool Mike Shor

Self-Selection Only high risk drivers “self-select” into the contract to buy insurance Screening sets up the proper incentives for individuals to self-select Pooling has the danger of adverse selection Mike Shor

Adverse Selection Imagine ½ of the population are high-risk drivers
Insurance company calculates expected cost of not having a deductible: (1/2) (10%) \$ (1/2) (30%) \$1000 = \$200 Add a 10% profit, charge \$220 Only high risk drivers sign up! Mike Shor

How to Screen Want to know an unobservable trait
Identify an action that is more costly for “bad” types than “good” types Ask the person (are you “good”?) But… attach a cost to the answer Cost high enough so “bad” types don’t lie Low enough so “good” types don’t lie Mike Shor

Screening Education as a signaling and screening device
Is there value to an economics degree? Imagine not: no effect on productivity, but is observed by employers “Cost” of economics major varies Mike Shor

Example: Econ majors How hard should an econ major be?
Two types of workers: High and low quality NPV of salary high quality worker: \$900,000 low quality worker: \$700,000 Disutility per econ credit high quality worker: \$4,000 low quality worker: \$6,000 Mike Shor

“High” Quality Workers
If I get an econ major: Signal I am a high quality worker Receive \$900,000 - \$4,000 N If I don’t get an econ major Signal I am a low quality worker Receive \$700,000 900,000 – 4,000 N > 700,000 200, > 4,000 N 50 credits > N Mike Shor

“Low” Quality Workers 900,000 – 6,000 N < 700,000
If I get an econ major: Signal I am a high quality worker Receive \$900,000 - \$6,000 N If I don’t get an econ major Signal I am a low quality worker Receive \$700,000 900,000 – 6,000 N < 700,000 200, < 6,000 N 33 credits < N Mike Shor

Screening To achieve a separating equilibrium:
Costly enough to deter low types Not so costly as to deter high types High reward High reward – high-type cost – low-type cost > Low reward < Low reward Mike Shor

Screening To achieve a separating equilibrium:
High types work for high reward Low types accept low reward High reward High reward – Low reward – Low reward > high-type cost < low-type cost Mike Shor

Screening Solves Market Imperfections
Market for lemons (used cars) Worth between \$1000 and \$3000 to buyers Worth \$200 less to sellers Only seller knows true value Buyer offers \$2,000  Adverse selection Only cars between \$1,000 and \$2,200 sold Buyer offers \$1,600  Adverse selection Only cars between \$1,000 and \$1,800 sold Market equilibrium price: \$1,200 Only worst 20% of cars are ever sold Mike Shor

Screening Solves Market Imperfections
Market for lemons What about introducing a screen? Extended warranty Cheaper to provide for good cars than bad cars Other examples Coupons Banks made of granite Mike Shor

Hiding from Signals The opportunity to signal may prevent some types from hiding their characteristics Examples: Financial disclosures GPA on résumé Taking classes pass / fail Mike Shor

Hiding from Signals Suppose students can take a course pass/fail or for a letter grade. An A student should signal her abilities by taking the course for a letter grade – separating herself from the population of B’s and C’s. This leaves B’s and C’s taking the course pass/fail. Now, B students have incentive to take the course for a letter grade to separate from C’s. Ultimately, only C students take the course pass/fail. If employers are rational – will know how to read pass/fail grades. C students cannot hide! Mike Shor

Summary Enticing high effort is hard work Screening Leakages
Global vs. individual incentives Rewarding the right people Screening Identify unobservable cost differences Exploit them (carefully) Mike Shor

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